How does a mortise chisel work?

Are we talking about the kind of chisel that is intended for hand use or the type that's an attachment to a drill press. Let's talk about what a mortise traditionally is; a deep "socket" to accept a tenon.

A chisel used to cut a mortise is shaped differently than one used for general woodworking. The sides are parallel to keep the cut straight and the it's taller than it is wide.

Many woodworkers will use a drill to remove the bulk of the wood inside the mortise just to speed things up but you can chop out the wood entirely with the chisel.

If you're talking about the type that's used with a drill press, then the drill bit inside the chisel removes the bulk of the material while the chisel on the outside squares up the edges/corners. It must be used with a drill press.